Erfan Panahi 810198369

Final Prohect

Linear Algebra

clc
clear
close all

Problem 2.

Image Compression (Gray-scale Image):

img1 = imread('1.tiff');

img1_gray = rgb2gray(img1);

Image_Comparing(img1_gray);

img2 = imread('2.tiff');

img2_gray = rgb2gray(img2);

Image_Comparing(img2_gray);

img3 = imread('3.tiff');

img3_gray = rgb2gray(img3);

Image_Comparing(img3_gray);

img4 = imread('4.tiff');

img4_gray = rgb2gray(img4);

Image_Comparing(img4_gray);

img5 = imread('5.tiff');

img5_gray = rgb2gray(img5);

Image_Comparing(img5_gray);

Image Compression (Colored Image):

Image_Comparing_colored(img1);

Image_Comparing_colored(img2);

Image_Comparing_colored(img3);

Image_Comparing_colored(img4);

Image_Comparing_colored(img5);

Image Denoising: (Using SVD)

img1_noisy = imread('1.jpeg');

SVD_denoising_plot(img1_noisy)

img2_noisy = imread('2.jpeg');

SVD_denoising_plot(img2_noisy)

img3_noisy = imread('3.jpeg');

SVD_denoising_plot(img3_noisy)

img4_noisy = imread('4.jpeg');

SVD_denoising_plot(img4_noisy)

img5_noisy = imread('5.jpeg');

SVD_denoising_plot(img5_noisy)

Image Denoising: (Using FFT)

FFT_denoising_plot(img1_noisy)

FFT_denoising_plot(img2_noisy)

FFT_denoising_plot(img3_noisy)

FFT_denoising_plot(img4_noisy)

FFT_denoising_plot(img5_noisy)

function [compressed_img] = compress_img_svd(img, k)
    [U,S,V] = svd(double(img));
    n = ceil(size(S,2)*k);
    S_new = S * diag([ones(1,n) ,zeros(1, size(S,2)-n)]);
    compressed_img = uint8(U*S_new*V');
end
function [compressed_img] = compress_img_svd_colored(img, k)
    compressed_img = img;
    for i = 1:3
        compressed_img(:,:,i) = compress_img_svd(img(:,:,i), k);
    end
end
function [compressed_img] = compress_img_fft(img, k)
    img_f = fft2(img);
    img_f_sorted = sort(abs(img_f(:)));
    thr = img_f_sorted(ceil((1-k)*length(img_f_sorted)));
    img_cmp = ifft2((abs(img_f) > thr) .* img_f);
    compressed_img = uint8(img_cmp);
end
function [compressed_img] = compress_img_fft_colored(img, k)
    compressed_img = img;
    for i = 1:3
        compressed_img(:,:,i) = compress_img_fft(img(:,:,i), k);
    end
end
function Image_Comparing(img)
    K = [12, 10, 8, 4, 1, 0.5, 0.1] / 100;
    f = figure;
    f.Position = [10 10 5000 1000];
    for i = 1:7
        subplot(2,7,i)
        imshow(compress_img_svd(img, K(i)))
        title(['SVD (coff = ',num2str(K(i)),')'],'Interpreter','latex')
        subplot(2,7,i+7)
        imshow(compress_img_fft(img, K(i)))
        title(['FFT (coff = ',num2str(K(i)),')'],'Interpreter','latex')
    end
end
function Image_Comparing_colored(img)
    K = [12, 10, 8, 4, 1, 0.5, 0.1] / 100;
    f = figure;
    f.Position = [10 10 5000 1000];
    for i = 1:7
        subplot(2,7,i)
        imshow(compress_img_svd_colored(img, K(i)))
        title(['SVD (coff = ',num2str(K(i)),')'],'Interpreter','latex')
        subplot(2,7,i+7)
        imshow(compress_img_fft_colored(img, K(i)))
        title(['FFT (coff = ',num2str(K(i)),')'],'Interpreter','latex')
    end
end
function [img_rec] = SVD_denoising(colored_img, thr)
    img_rec = colored_img;
    for i = 1:size(colored_img,3)
        img = colored_img(:,:,i);
        [U,S,V] = svd(double(img));
        x = diag(S);
        y = x(1:end-1)-x(2:end);
        S_new = diag(x .* [(y>thr);0]);
        img_rec(:,:,i) = uint8(U*S_new*V');
    end
end
function SVD_denoising_plot(colored_img)
    Thr = [1, 1.5, 2, 2.5, 3];
    figure
    subplot(2,3,1)
    imshow(colored_img)
    title('Noisy Image','Interpreter','latex')
    for i = 1:length(Thr)
        subplot(2,3,i+1)
        imshow(SVD_denoising(colored_img, Thr(i)))
        title(['SVD denoising (thr = ',num2str(Thr(i)),')'],'Interpreter','latex')
    end
end
function [img_rec] = FFT_denoising(colored_img, r)
    img_rec = colored_img;
    for i = 1:size(colored_img,3)
        img = colored_img(:,:,i);
        n = floor(r * size(img,2));
        img_f = fft2(img);
        img_f(:,n:end-n) = 0;
        img_f(n:end-n,:) = 0;
        img_rec(:,:,i) = uint8(real(ifft2(img_f)));
    end
end
function FFT_denoising_plot(colored_img)
    R = [0.3, 0.35, 0.4, 0.45, 0.49];
    figure
    subplot(2,3,1)
    imshow(colored_img)
    title('Noisy Image','Interpreter','latex')
    for i = 1:length(R)
        subplot(2,3,i+1)
        imshow(FFT_denoising(colored_img, R(i)))
        title(['FFT denoising (r = ',num2str(R(i)),')'],'Interpreter','latex')
    end
end